Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence

A Tree Logic with Graded Paths and Nominals

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time

Expressive Logical Combinators for Free

International audienceA popular technique for the analysis of web query languages relies on the translation of queries into logical formulas. These formulas are then solved for satisfiability using an off-the-shelf satisfiabil-ity solver. A critical aspect in this approach is the size of the obtained logical formula, since it constitutes a factor that affects the combined complexity of the global approach. We present logical combi-nators whose benefit is to provide an exponential gain in succinctness in terms of the size of the logical representation. This opens the way for solving a wide range of problems such as satisfiability and containment for expressive query languages in exponential-time, even though their direct formulation into the underlying logic results in an exponential blowup of the formula size, yielding an incorrectly presumed two-exponential time complexity. We illustrate this from a practical point of view on a few examples such as numerical occurrence constraints and tree frontier properties which are concrete problems found with semi-structured data

Blazes: Coordination Analysis for Distributed Programs

Distributed consistency is perhaps the most discussed topic in distributed systems today. Coordination protocols can ensure consistency, but in practice they cause undesirable performance unless used judiciously. Scalable distributed architectures avoid coordination whenever possible, but under-coordinated systems can exhibit behavioral anomalies under fault, which are often extremely difficult to debug. This raises significant challenges for distributed system architects and developers. In this paper we present Blazes, a cross-platform program analysis framework that (a) identifies program locations that require coordination to ensure consistent executions, and (b) automatically synthesizes application-specific coordination code that can significantly outperform general-purpose techniques. We present two case studies, one using annotated programs in the Twitter Storm system, and another using the Bloom declarative language.Comment: Updated to include additional materials from the original technical report: derivation rules, output stream label

Effects for Efficiency: Asymptotic Speedup with First-Class Control

We study the fundamental efficiency of delimited control. Specifically, we show that effect handlers enable an asymptotic improvement in runtime complexity for a certain class of functions. We consider the generic count problem using a pure PCF-like base language $\lambda_b$ and its extension with effect handlers $\lambda_h$. We show that $\lambda_h$ admits an asymptotically more efficient implementation of generic count than any $\lambda_b$ implementation. We also show that this efficiency gap remains when $\lambda_b$ is extended with mutable state. To our knowledge this result is the first of its kind for control operators